Symbolic Mathematics in Artificial Intelligence

1. Artificial Intelligence

2. Symbolic Mathematics
Solving Algebra Problems

3. SYMBOLIC MATHEMATICS:
 In mathematics and computerscience it is a scientific area it
is refers to the study and development of algorithms and
software for manipulating mathematical expressions.
 Symbolic calculations use symbols. Symbolic computation is the sub-area
of the mathematicsand computer science which solve symbolic problems
on symbolic objects representable on computer.
Examples:
Algebraic expressions
Logical prepositions
Programs

4. SYMBOLIC MATHEMATICS:
 Symbolic AI was the dominant technique of AI research from
the mid- 1950s until the middle 1990s.
 One of the best-known symbolic mathematics software
packages is mathematica.
 Other include ESP, AXIOM*, MAT-LAB.

5. History of AI, the research field is divided into two camps
Symbolic AI Non-symbolic AI
• Symbolists firmly believed in
developing an intelligent system
based on rules and knowledge
and whose actions were
interpretable.
• Non-symbolic approach strived to
build a computational system
inspired by the human brain.

6. Symbolic Mathematics Finally Yields
To Neural Networks
 By translating symbolic math into tree-like structures, neural
networks can finally begin to solve more abstract problems.
 To allow a neural network to process the symbols like a mathematician,
charton and lample began by translating mathematical expressions into more
useful forms.
 They ended up re-interpreting them.
 Mathematical operators such as addition, subtraction, multiplication and
division became junctions on the tree.
 For almost all the problems, the program took less than 1 second to generate
correct solutions.

7. Symbolic Mathematics Finally Yields
To Neural Networks

8. SOLVING ALGEBRA PROBLEMS
 STUDENT:
• STUDENT was another early language understanding program, written by
daniel bobrow as his Ph.D. Research project in 1964.
• It was designed to read and solve the kind of word problems found
in high school algebra books.
• An example is:
• If the number of customers tom gets is twice the square of 20% of the number of
advertisements he runs, and the number of advertisements is 45, then what is
the number of customers tom gets?
• Student could correctly reply that the number of customers is 162.

9. STUDENT: SOLVING ALGEBRA PROBLEMS
 To do this, STUDENT must be far more sophisticated than ELIZA; it must
process and “understand” a great deal of the input, rather than just
concentrate on a few key words.
 STUDENT program uses little more than the pattern- matching
techniques of ELIZA to translate the input into a set of algebraic equations.
From there, it must know enough algebra to solve the equations, but that
is not very difficult.
 And it must compute a response, rather than just fill in blanks.

10. SOLVING ALGEBRA PROBLEMS
The real work is done by solve, which has the following specification:
(1) Find an equation with exactly one occurrence of an unknown in it.
(2) Transform that equation so that the unknown is isolated on the left-hand side. This
can be done if we limit the operators to +, -,*,and /.
(3) Evaluate the arithmetic on the right-hand side, yielding a numeric value for the
unknown.
(4) Substitute the numeric value for the unknown in all the other equations, and
remember the known value. Then try to solve the resulting set of equations.
(5) If step (1) fails—if there is no equation with exactly one unknown—then just return
the known values and don’t try to solve anything else.